Physics H131: Hints for Problem Set #9

Chapter C13 Problems

• C13B.8: Where does the force from the cord act? Which way does it point? In which direction will you apply force to the rim? Which quantity are you trying to balance, the force or ...?
• C13S.5: This is a "rolling without friction" problem. How do you calculate the moment of inertia of the pipe? Can you make the approximation of a thin cylindrical shell (hoop), or should you try to compute it from the difference between two solid cylinders with different radii?
• C13R.2: Solve the problem algebraically first. A lot of parameters that you don't know and might want to guess may drop out from the final solution. It turns out (surprisingly) that everything you really need to know is given in the problem statement. Compute the k-work done by the friction force on the wheel. Into which forms of energy is this k-work converted? Use the idea of torque as the "tool" to change the angular momentum of the wheels. What are the initial and final angular momenta of the wheel? How can you exploit this to calculate the magnitude of the friction force (assuming that is constant in time)?
• C13A.2: Decompose the two vectors into x,y,z-components, using a representation with unit vectors. Then work out the 9 terms, using the cross products among the unit vectors.

Chapter C14 Problems

• C14T.3: Look carefully at Eq. (C14.6). How do the proposed design changes affect each of the factors entering in this formula?
• C14T.5: What does momentum conservation tell you? What else does it tell you about the force from the ball acting on the arm? Where does this force apply? In which direction does the torque resulting from this force point?
• C14B.2: This is similar to C14T.1, which we did in class.
• C14S.3: Use angular momentum conservation!
• C14S.5: How does angular momentum conservation relate the angular momenta of the cat and of the turntable?
• C14R.1: Draw a couple of pictures! Use energy and momentum conservation as well as angular momentum conservation. How does the center of mass of the system move? Write down all energy contributions before and after the collision. For calculating moments of inertia, model the fighter plane as a mass point and the cruiser as a rod. To simplify the calculation, you may neglect the displacement between the center of mass of the entire system and the center of mass of the cruiser just before the collision and use the latter as the reference point for calculating the angular momenta before and after the collision.
  [If you don't neglect this displacement, the linear motion of the system's center of mass relative to your reference point contributes to the total angular angular momentum. In this case it might be easier to use the system's center of mass as reference point; this means that you would be using a moving inertial reference frame, and you would have to recalculate the fighter's and cruiser's initial speeds in that reference frame in order to compute the initial total angular momentum. Calculation of the final angular momentum would be a lot easier in that frame, though.]